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A326117 Number of subsets of {1..n} containing no products of two or more distinct elements.

%I A326117 #10 Apr 11 2021 23:51:20
%S A326117 1,2,3,5,9,17,29,57,101,201,365,729,1233,2465,4593,8297,15921,31841,
%T A326117 55953,111905,195713,362337,697361,1394721,2334113,4668225,9095393,
%U A326117 17225313,31242785,62485569,106668609,213337217,392606529,755131841,1491146913,2727555425,4947175713
%N A326117 Number of subsets of {1..n} containing no products of two or more distinct elements.
%C A326117 If this sequence counts product-free sets, A326081 counts product-closed sets.
%H A326117 Fausto A. C. Cariboni, <a href="/A326117/b326117.txt">Table of n, a(n) for n = 0..47</a>
%F A326117 For n > 0, a(n) = A326116(n) + 1.
%e A326117 The a(6) = 28 sets:
%e A326117   {}  {1}  {2,3}  {2,3,4}  {2,3,4,5}
%e A326117       {2}  {2,4}  {2,3,5}  {2,4,5,6}
%e A326117       {3}  {2,5}  {2,4,5}  {3,4,5,6}
%e A326117       {4}  {2,6}  {2,4,6}
%e A326117       {5}  {3,4}  {2,5,6}
%e A326117       {6}  {3,5}  {3,4,5}
%e A326117            {3,6}  {3,4,6}
%e A326117            {4,5}  {3,5,6}
%e A326117            {4,6}  {4,5,6}
%e A326117            {5,6}
%t A326117 Table[Length[Select[Subsets[Range[n]],Intersection[#,Select[Times@@@Subsets[#,{2}],#<=n&]]=={}&]],{n,0,20}]
%Y A326117 Cf. A007865, A051026, A103580, A196724, A326020, A326023, A326076, A326078, A326079, A326081, A326116, A308542.
%K A326117 nonn
%O A326117 0,2
%A A326117 _Gus Wiseman_, Jun 06 2019
%E A326117 Terms a(21)-a(36) from _Andrew Howroyd_, Aug 30 2019